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GATE 2021 CY – Question 7

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

Consider two rectangular sheets, Sheet M and Sheet N of dimensions 6 cm x 4 cm each. Folding operation 1: The sheet is folded into half by joining the short edges of the current shape. Folding operation 2: The sheet is folded into half by joining the long edges of the current shape. Folding operation 1 is carried out on Sheet M three times. Folding operation 2 is carried out on Sheet N three times. The ratio of perimeters of the final folded shape of Sheet N to the final folded shape of Sheet M is ______.

  1. 13 : 7
  2. 3 : 2
  3. 7 : 5
  4. 5 : 13

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Correct answer: (A) 13 : 7

Explanation

Operation 1 halves the longer dimension of the current rectangle: M goes 6×4→3×4→3×2→1.5×2, with perimeter 7 cm. Operation 2 halves the shorter dimension: N goes 6×4→6×2→6×1→6×0.5, with perimeter 13 cm. The required N:M ratio is **13:7, A**.